Abstract:
Consider a random smooth Gaussian field G(x):F→R, where F is a compact in Rd. We derive a formula for average area of a surface set by the equation G(x)=0 and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of any non-random smooth field. Bibl. 13 titles.
Key words and phrases:
random Gaussian field, surface area, Favard measure, coarea formula, Rice formula.
Citation:
D. N. Zaporozhets, I. A. Ibragimov, “On random surface area”, Probability and statistics. Part 16, Zap. Nauchn. Sem. POMI, 384, POMI, St. Petersburg, 2010, 154–175; J. Math. Sci. (N. Y.), 176:2 (2011), 190–202
\Bibitem{ZapIbr10}
\by D.~N.~Zaporozhets, I.~A.~Ibragimov
\paper On random surface area
\inbook Probability and statistics. Part~16
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 384
\pages 154--175
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3888}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 176
\issue 2
\pages 190--202
\crossref{https://doi.org/10.1007/s10958-011-0409-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959538404}
Linking options:
https://www.mathnet.ru/eng/znsl3888
https://www.mathnet.ru/eng/znsl/v384/p154
This publication is cited in the following 5 articles:
A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583
V. I. Bernik, N. V. Budarina, A. V. Lunevich, Kh. O'Donnell, “Raspredelenie nulei nevyrozhdennykh funktsii na korotkikh otrezkakh II”, Chebyshevskii sb., 19:1 (2018), 5–14
V. I. Bernik, N. V. Budarina, A. V. Lunevich, Kh. O'Donnel, “Raspredelenie nulei nevyrozhdennykh funktsii na korotkikh otrezkakh”, Chebyshevskii sb., 18:4 (2017), 107–115
Pavel Bleher, Yushi Homma, Roland K. W. Roeder, “Two-Point Correlation Functions and Universality for the Zeros of Systems of SO(n+1)-invariant Gaussian Random Polynomials”, Int Math Res Notices, 2016:11 (2016), 3237
A. P. Shashkin, “Functional limit theorem for integrals over level sets of Gaussian random field”, Theory Probab. Appl., 60:1 (2016), 150–161
Citation in format AMSBIB
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